The most common digit in the decimal form of 7^n; the least one if there are duplicates.
1, 7, 4, 3, 0, 0, 1, 3, 0, 0, 2, 7, 1, 0, 2, 4, 3, 2, 1, 1, 2, 5, 8, 3, 1, 6, 3, 3, 9, 7, 2, 4, 2, 7, 6, 6, 1, 1, 1, 0, 0, 0, 3, 3, 6, 0, 4, 3, 1, 2, 4, 5, 1, 6, 4, 5, 6, 1, 4, 1, 2, 5, 4, 0, 1, 0, 9, 4, 1, 0, 6, 4, 2, 2, 2, 0, 1, 8, 0, 8, 0, 0, 2, 9, 0, 2, 9
0
Sequence S000178 gives the number of such digits in 7^n.
T. D. Noe, Plot of 1001 terms
T. D. Noe, Table of 1001 terms
(Mma) Table[s = RotateRight[DigitCount[7^n]]; Position[s, Max[s], 1, 1][[1, 1]] - 1, {n, 0, 100}]
nonn,base
T. D. Noe, Aug 06 2014